official quant thread for cat08

[anil.iitkgp]

Originally Posted by implex

x=-1,5 y=-2,8

x/y min will be -5/2

ya missed the logic. thanks implex..

[hi.shivani]

Q3)If mod(x)-mod(y)=13,which of the following can’t be true value of x-y?
a) -18 b) -9 c) -17 d) None of these

Q4) Let y=max(x+3),(7-2x),minimum value of y for 2≥x≥1?
a) 4.5 b) 4.0 c) 4.67 d) 4.33

[hi.shivani]

Originally Posted by implex

one lines use Am-GM
answer is 4

meaning ????

[Matrix7]

[quote=hi.shivani;1175181]Q3)If mod(x)-mod(y)=13,which of the following can’t be true value of x-y?
a) -18 b) -9 c) -17 d) None of these

*********************
Solution

There are four possible cases.

Case 1: x=>0, y=>0
Hence, we have x-y=13

Case 2: x<0, y=>0
Hence, we have -x-y=13 or x+y=-13
This is compatible with x-y=-18 giving x=-15.5 and y=2.5
It is also compatible with x-y=-17 giving x=-15 and y=2
It is not compatible with x-y=-9 since that gives x=-11 and y=-2

Case 3: x<0, y<0
Hence, we have -x+y=13 or x-y=-13

Case 4: x=>0, y=>0
Hence, we have x+y=13
This is not compatible with x-y=-18 or x-y=-17 or x-y=-9

Thus the correct answer is option (b) -9.

[implex]

Originally Posted by hi.shivani

meaning ????

[4^x+4^(1-x)]/2>=sqrt[(4^x.4^(1-x)]=sqrt(4)=2
so [4^x+4^(1-x)]>=4

[hi.shivani]

Originally Posted by implex

[4^x+4^(1-x)]/2>=sqrt[(4^x.4^(1-x)]=sqrt(4)=2
so [4^x+4^(1-x)]>=4

hey rahul i ws asking wr z the am /gm

[jha16june]

Originally Posted by implex

New Problem 222)
Two friends get home at 2:30 P.M. They both go to bed 10 P.M. If both friends will go to a park twice for 15 minutes, what is the probability that they will be able to see each other at any random time between the two time intervals? Assume that the travel to and from the park takes no time.
a) 25/225 b) 8/15 c) 27/225 d) 29/225 e)3/17

Beautiful problem from Aops. I have posted an original solution there

Answer is d) 29/225
This kind of problem has already been discussed in the thread.

[implex]

Originally Posted by hi.shivani

hey rahul i ws asking wr z the am /gm

arithmetic mean of positive numbers is always greater than or equal to the geometric mean of the same set of numbers. The equality holds when all the numbers are equal

[implex]

Originally Posted by jha16june

Answer is d) 29/225
This kind of problem has already been discussed in the thread.

oh i may have missed, this problem is a bit different though. the arrival twice needs to be considered

[hi.shivani]

Q) Let y=max(x+3),(7-2x),minimum value of y for 2≥x≥1?
a) 4.5 b) 4.0 c) 4.67 d) 4.33

Q) Minimum value of 3x+3y+zsubjected to the condition xyz=24, when x, y, z are all positive numbers is
a) 14 x 3^(1/3) b) 18 c) 216 d) 12